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The most important part of the Federal Reserve-watching game is now this: figuring out how long it will take for the unemployment rate to drop to 6.5 percent. That's the benchmark that the Fed's rate-setting Open Market Committee pegged in December as the one that will prompt it to begin raising the Fed funds rate, now set between 0 and a quarter of a percentage point.

Two new pieces of research — one from Morgan Stanley, one from CNBC — suggest it could be years, in fact, at least a half a decade, before the economy hits that mark. Both projections require a series of assumptions that are unlikely to be accurate: principally that there is no recession over an extended period and that job growth or economic growth remains steady. But they are still useful as a way to think about how long the Fed could keep rates on hold and, by extension, how long before the Fed stops buying assets through quantitative easing. The Fed has said that it would do so "if the outlook for the labor market does not improve substantially," a phrase that has been taken to mean some unemployment rate below the current level of 7.8 percent but above the 6.5-percent trigger for raising rates.

Here are two different ways of projecting how long it could take until that 6.5-percent unemployment rate is reached.

He assumed different monthly job growth rates and different participation rates — the percentage of the working age population that says they are part of the workforce. (See sidebar on the participation rate). He found that if the participation rate remains the same at 63.6 percent, and the economy adds 150,000 jobs a month, then it will take about 6.5 years to reach the magic 6.5 percent unemployment rate.

If the participation rate drops further, which some economists predict, then that date could be sooner. At a 63.2 rate, unemployment could hit the Fed's metric near the end of next year. But if a rebounding economy brings people back into the work force, and the participation rate rises, but these people don't find work immediately, then the arrival of 6.5-percent unemployment rate will be pushed ahead. For example, if the participation rate climbs back to where it was just last year — 64.2 — it would take 16 years of monthly job growth at 150,000 per month to get down to 6.5 percent unemployment. Of course, higher monthly job growth in the range of 200,000 or 300,000 a month would dramatically shorten the time to get the unemployment down into the Fed's range for action on its interest rate.

CNBC

CNBC Estimate

CNBC took a different tack of trying to figure out how the Fed connects growth rates with projected declines in unemployment rates. We used the Fed's economic projections over the past five years to estimate how much of a decline in the unemployment rate is associated with given levels of growth in gross domestic product.

Not surprisingly, the data show that the higher the level of GDP, the more the Fed believes the unemployment rate will decline. (No one, as far as we know, had ever estimated by how much.) The estimates shows the economy has to ratchet up growth substantially from current levels in order to achieve a 6.5-percent unemployment rate.

For example, at growth rates between 2.25 and 2.75 percent, the Fed on average forecasts that unemployment rate will fall by 0.2 percentage points a year. At that rate, it will take 5.8 years to get down to 6.5 percent. (Note that the CNBC estimate does not take into account changes in the participation rate since it can't be determined what rate Fed forecasters are using.) The economy has grown at only around 2 percent the past several years. The estimate assumes no recession over the time period.

But if growth would surge into the range of 3.25 to 3.75 percent, then we could hit 6.5-percent unemployment by around the end of 2015, with the rate falling about 0.6 percent a year, according to the CNBC estimate. And if we should hit a level of around 4-percent annual growth, 6.5-percent unemployment would come in the first or second quarter of 2014.

The average Fed forecast is for unemployment to drop to 6.3 percent in 2015. Of the committee's 19 members, 13 see the first rate hike in that year.